16 citations · 81 across the 20 of their papers we have counts for
13 papers · 1 filter
A simple stability analysis of the Lanczos algorithm in finite precision arithmetic
Tyler Chen
We give a self-contained analysis of the symmetric Lanczos algorithm without reorthogonalization when computations are performed inexactly. We show the computed Lanczos vectors are…
The Lanczos algorithm for matrix functions: a handbook for scientists
Tyler Chen
Lanczos-based methods have become standard tools for tasks involving matrix functions. Progress on these algorithms has been driven by several largely disjoint communities, resulti…
Optimal Polynomial Approximation to Rational Matrix Functions Using the Arnoldi Algorithm
Tyler Chen, Anne Greenbaum, Natalie Wellen
Given an by matrix and an -vector , along with a rational function , we show how to find the optimal approximation to from the K…
GMRES, pseudospectra, and Crouzeix's conjecture for shifted and scaled Ginibre matrices
Tyler Chen, Anne Greenbaum, Thomas Trogdon
We study the GMRES algorithm applied to linear systems of equations involving a scaled and shifted matrix whose entries are independent complex Gaussians. When the righ…
Nearly Optimal Approximation of Matrix Functions by the Lanczos Method
Noah Amsel, Tyler Chen, Anne Greenbaum +2
Approximating the action of a matrix function on a vector is an increasingly important primitive in machine learning, data science, and statistics, wit…
Stability of the Lanczos algorithm on matrices with regular spectral distributions
Tyler Chen, Thomas Trogdon
We study the stability of the Lanczos algorithm run on problems whose eigenvector empirical spectral distribution is near to a reference measure with well-behaved orthogonal polyno…
A posteriori error bounds for the block-Lanczos method for matrix function approximation
Qichen Xu, Tyler Chen
We extend the error bounds from [SIMAX, Vol. 43, Iss. 2, pp. 787-811 (2022)] for the Lanczos method for matrix function approximation to the block algorithm. Numerical experiments…
Krylov-aware stochastic trace estimation
Tyler Chen, Eric Hallman
We introduce an algorithm for estimating the trace of a matrix function using implicit products with a symmetric matrix . Existing methods for implicit…
Randomized matrix-free quadrature: unified and uniform bounds for stochastic Lanczos quadrature and the kernel polynomial method
Tyler Chen, Thomas Trogdon, Shashanka Ubaru
We analyze randomized matrix-free quadrature algorithms for spectrum and spectral sum approximation. The algorithms studied include the kernel polynomial method and stochastic Lanc…
Low-memory Krylov subspace methods for optimal rational matrix function approximation
Tyler Chen, Anne Greenbaum, Cameron Musco +1
We describe a Lanczos-based algorithm for approximating the product of a rational matrix function with a vector. This algorithm, which we call the Lanczos method for optimal ration…
Error bounds for Lanczos-based matrix function approximation
Tyler Chen, Anne Greenbaum, Cameron Musco +1
We analyze the Lanczos method for matrix function approximation (Lanczos-FA), an iterative algorithm for computing when is a Hermitian matri…
On the Convergence Rate of Variants of the Conjugate Gradient Algorithm in Finite Precision Arithmetic
Anne Greenbaum, Hexuan Liu, Tyler Chen
We consider three mathematically equivalent variants of the conjugate gradient (CG) algorithm and how they perform in finite precision arithmetic. It was shown in [{\em Behavior of…
Predict-and-recompute conjugate gradient variants
Tyler Chen, Erin C. Carson
The standard implementation of the conjugate gradient algorithm suffers from communication bottlenecks on parallel architectures, due primarily to the two global reductions require…